3 FI & FX

3.1 Fixed Income

3.1.1 Bond Calculator in R

3.1.1.1 Calculate Forward Rates

Calculate Forward Rates

Create a table with bond (or import real ones) and calculate forward rates.

library(dplyr) 
#Calculate Forward rate 
#Create a table with plain vanilla bonds
df <- tribble( 
  ~bond, ~maturity, ~yield, 
  1, 1.5, 1.65, 
  2, 3, 1.55, 
  3, 5, 1.8, 
  4, 10, 1.9 
) 
#Create table with all bonds in columns for short vs long bond
df <- df %>% 
  mutate(dummy = 1L) %>% 
  inner_join(., ., by = "dummy", suffix=c("_short", "_long")) %>% 
  select(-dummy) %>% 
  filter(bond_short < bond_long) 
#Create column with maturity for length between bonds (not neccesary for below calculation)
df <- mutate(df, maturity_between_bonds = (maturity_long  - maturity_short))
day_count <- 360
#Create function for calculating frw rate
calculate_forward_rate <- function(maturity_short, yield_short, maturity_long, yield_long, day_count){
  
  short_bond <- (1+yield_short/100)^(maturity_short/day_count)
  long_bond <- (1+yield_long/100)^(maturity_long/day_count)
  days_between <- (maturity_long - maturity_short)
  forward_rate <- ((long_bond/short_bond)^(360/days_between)-1)*100
  return(round(forward_rate, digits=2))  
}
#run function
df <- df %>%
  mutate(forward_rate = calculate_forward_rate(
    maturity_short,
    yield_short,
    maturity_long,
    yield_long,
    day_count))
#Create a yield_diff. How much more/less the yield must be when its time to buy the subsequent bond       
df <- df %>%
  mutate(yield_diff = if_else(bond_short == bond_long, NA_real_, forward_rate - yield_short))

3.1.1.2 Bond Converter

Calculate Bond Price

Maturity <- "2023-04-30"
  Handle <- 100
  x32 <- 25
  x64 <- 24
  cpn <- 2.25
  
  ttm <- as.numeric(as.Date(Maturity) - as.Date(Sys.Date())) / 365
  FV <- 100
  
  calculate_price <- function(Handle, x32, x64){
    bond_price <- Handle + ((x32+(x64/64))/32)
    return(format(round(bond_price,10), nsmall=10))
  }
  
 bond_price <- as.numeric(calculate_price(Handle, x32, x64))

Convert from Discount to Yield

  discount  <- 1.69
  maturity_date <- as.Date("2021-05-06")
  settlement_date <- Sys.Date() +1
  day_count <- 360
  calculate_ytm_from_discount <- function(discount, maturity_date, settlement_date, day_count){
 
    days <- as.numeric(maturity_date-settlement_date)
    discount <- discount / 100
      yield_ <- (discount / (1-(discount * (days/day_count))))
    return(format(round(yield_*100,10),nsmall=10))
  }
  
  calculate_ytm_from_discount(discount, maturity_date, settlement_date, day_count)

Convert from Yield to Discount

  yield  <- 1.719967
  maturity_date <- as.Date("2021-05-06")
  settlement_date <- Sys.Date()+1
  day_count <- 360
  yield <- yield / 100
  calculate_disc_from_yield <- function(yield, maturity_date, settlement_date, day_count){
    
    days <- as.numeric(maturity_date-settlement_date)
 
    discount <- (yield / (1+(yield /(day_count/days))))
    return(format(round(discount*100,10),nsmall=10))
  }
  
  calculate_disc_from_yield(yield, maturity_date, settlement_date, day_count)

3.2 Foreign Exchange